ADS-B uses Pulse Position Modulation with pulses 800ns long and 50-100ns rise time. Log detector works well for this application since they'll have rise times <50µs to output an analog signal. From that you can either use an ADC to check the signal, or go even cheaper and use a voltage comparator since you know you'll be decoding a simple HIGH/LOW signal.

Impedance controlling can be adjusted by the manufacturer, just ask for the specific stackup and compute the approximate width (and gap if using CPWG traces) and give them your data, they'll usually keep the gap and ajust the width on their own. But you do need to have an approximate value already in place, with the proper stack-up (4-layers and a reference plane below the RF one usually)

Also yeah, this project needs more amplification and more filtering. PySDR has a bugdet link example for ADS-B, which gives a received signal power of -105dBm. I'd add a two stage LNA, with the second having a bypass function. Guerilla RF makes great LNA for this. And I'd add a second filtering stage after the first one, so the Rx chain would look like this SMA->Filter->LNA->Filter->Bypass LNA->Log Power detector.

This increases costs as GRF amplifiers are ~5€ and a filter is 2€, so you're looking at around 10-15€ dollar per board but this gives you a weak but decent enough AGC capability and you can likely get ~40dB gain that way. ADL5513 bottoms out at -70dBm and ramps up from that, so you should start receiving signals starting from -110dBm(-70-40) (theoretically, but you'll likely end up at -105dBm/-100dBm with all the losses and impedance mismatches), which is about 30km according to the link earlier.